The amplitude damping channel is a fairly complete model for describing the decoherence effects suffered by superconducting qubits [1]}. To be more specific, it accurately models the quantum noise experienced by qubits that are said to be \(T_1\) -limited. In consequence, the time-varying amplitude damping (TVAD) channel was proposed in [2]}.
The Kraus operators for the TVAD channel for \(T_1\) -limited superconducting qubits are given by
\(E_0=\left( \begin{array}{cc}1 & 0\\0 & \sqrt{1-\gamma (t,\omega )} \end{array} \right),\;\;E_1=\left( \begin{array}{cc}0 & \sqrt{\gamma (t,\omega )}\\0 & 0 \end{array} \right),\) 
